After making the background transparent, can I...

After using these instructions (below) for making the background transparent for my logo, their is still a bit of white around a small section. Is their a way to remove the left over white?

- use select by color tool, with treshold of 0, no feathering and no antialiasing. Click on the background. This will select only pure white pixels in the background
- grow the selection by 2 pixels. The selection now includes the background, and the border pixels (anti-aliasing)
- use Color/Color to alpha with white (it will only applies to background and logo border)